Yes it is possible.
You can use sslh
sslh acts as a port protocol-demultiplexer, or reverse proxy in a way. It sniffs the first packet, determines the protocol and routes the traffic to the desired ip on the appropriate port as defined by your configuration file.
In my case I'm not able to open any other port than 80 and 443 (a common problem) so I already had sslh installed and demultiplexing ssh and https through port 443 and I wanted to add minecraft to that process. So I just edited the config file located for me (ubuntu 14.04/16.04)
etc/default/sslh to read as follows:
DAEMON_OPTS="--user sslh --listen 192.168.0.100:443 --ssh 127.0.0.1:22 --ssl 127.0.0.1:443 --anyprot 127.0.0.1:25565 --pidfile /var/run/sslh/sslh.pid"
The line is read sequentially, First it listens on the servers local ip on port 443 as passed to the server from my router, then it first looks for ssh traffic which is redirected to the loopback ip on port 22, then it looks for ssl/https traffic which is redirected to the loopback ip at port 443, then anything left over is sent to the minecraft port on the loopback ip.
In your case,with just one minecraft server you could just set the appropriate ip for the destination rather than the loopback ip (127.0.0.1) that I used.
If however you have multiple minecraft server subdomains you could, because the minecraft protocol includes the destination address in the first packet which includes the subdomain, write an appropriate regex sniff line for that packet explicitly, as described in the documentation, and subsequently send the individual traffic off to each ip as desired rather than just a different port on the loopback address as I did.
I didn't need to though since I only had one minecraft server and the "any other protocol" --anyprot flag and loopback address was sufficient for me.
Finally when I tested my_minecraft_server.mywebsite.tld:443 on this neat online minecraft status tester It worked. Yay.